Boolean Algebra Solver

Enter a boolean expression to generate its truth table.

AND: AB or A*B OR: A+B NOT: !A or A' XOR: A^B Parens: (A+B)C

Invalid Expression

What is Boolean Algebra?

Boolean Algebra is the mathematics of logic. Defined by George Boole in the 19th century, it is the foundation of all modern computing. Instead of numbers, it calculates with "Truth" (1) and "Falsehood" (0).

This solver parses your logic expression and generates a Truth Table showing every possible outcome.

Logic Gates & Operators

AND (High if ALL inputs High): A * B or AB. (Series circuit)

OR (High if ANY input High): A + B. (Parallel circuit)

NOT (Inverter): !A or A'. (Flips 1 to 0)

XOR (Uncommon inputs): A ^ B. (High if A is different from B)

Key Laws

De Morgan's First Law: !(A + B) = !A * !B (NOR is equivalent to ANDing inverted inputs).
De Morgan's Second Law: !(A * B) = !A + !B (NAND is equivalent to ORing inverted inputs).

Practical Applications

FPGA/CPLD Design: Hardware Description Languages (Verilog/VHDL) rely on reducing these expressions to save silicon area.
Software Logic: Simplifying complex if statements. if (!A && !B) is faster than if (!(A || B))? No, they are the same logic!

FAQ

What is SOP vs POS?

Sum of Products (SOP): ORing together ANDed terms (e.g. AB + CD). This maps directly to NAND-NAND logic. Product of Sums (POS): ANDing together ORed terms (e.g. (A+B)*(C+D)).

What is a Karnaugh Map (K-Map)?

A visual method to simplify boolean expressions by grouping 1s in a grid. It takes advantage of human pattern recognition to find the smallest possible logic circuit faster than algebraic reduction.

What is a "Minterm"?

A Minterm is a specific row in the truth table where the output is 1. If your truth table has 1s at rows 3, 5, and 7, the function is the "Sum of Minterms" m3 + m5 + m7.